A signature on a painting is important for a number of reasons. It shows that you are taking ownership of the painting, of course, but adding your signature to a painting is like adding a stamp to it that reads "finished." It's a sign that you're satisfied with the painting and no longer consider it a work in progress.
Is It Really Necessary to Sign a Painting?
It's not a legal requirement, of course, but if you don't add your name to a painting, how will anyone know who the artist is? You may argue that you have a very familiar style that people will recognize, but what if it's the first time someone's encountered your work? How will new observers find out?
If a piece of art is hanging in a gallery, it'll have a label with your name on it, but what if it's in someone's home and the owner can't remember who the artist was? Or those who purchased it might know, but their heirs might not, especially if it's not specifically scheduled in their will. Think about the works by famous artists that are "rediscovered" every now and then; is this a fate you want to risk for your paintings?
What Should My Signature Look Like?
The most important thing is that people must be able to read your signature. An illegible signature isn't a sign that you're extremely creative, and it doesn't add a level of intrigue to the painting. You're the artist, so let it be known. That said, don't make it look like you're using a stamp. It should not detract from the painting.
You don't have to sign your whole name on the front of the painting, you could just put your initials; if so, you'd be wise to put your full name on the back of the painting. The same applies if you use a symbol or an artist's monograph; people need to have some way of knowing what it stands for.
Should I Add a Date?
In most cases, you should put the date you finished a painting, though it needn't be next to your signature on the front. When you first start as an artist, you'll probably be able to remember what year you painted a particular piece. But after you've been painting for several years, you'll simply be unable to remember and will have to guess. Serious collectors and galleries like to be able to see how a painter's work developed over the years, so get into the habit now of dating your work. You don't have to put the date on the front of your painting but can write it on the back (though once it's framed you may not be able to see it). Or put only the year on the front and the month and year you completed it on the back.
Putting a date on a painting does not limit your potential to sell it. Art isn't like food. It has no sell-by date. If buyers wanted only the newest and latest works, then how come there's an auction market for contemporary paintings? If anyone asks why a painting from a few years back hasn't sold, tell them you kept it in your personal collection until now because you regard it as a key work.
Where Do I Put My Signature?
Signature location is up to you, though traditionally a signature is put toward one of the bottom corners. Be consistent about where you put your signature so that when people next encounter a painting they think is by you, they will know exactly where to check.
What Should I Use to Sign a Painting?
Use the same medium used in the painting to create your signature, whether it's pastel, watercolor—whatever. Sign the work before you clean your brushes and palette for the last time so you've got a suitable color on hand that will blend in with the work. A thin rigger brush is a good size and shape for signatures.
Having your signature "match" the painting, rather than having it look like a later addition, also makes it less likely that someone will question the authenticity of the work at some future date (after you're dead and your paintings have increased in value enormously). Avoid adding your signature on top of a layer of varnish, as it'll look like you forgot to do it in time. (Though if you must, keep it small and rather put your full signature on the back.)
Maiden Name or Married Name?
If you change your name when you get married, how should you sign your paintings? Should you continue using the name you had been, your maiden name, or should you change to your new, married name? Ultimately, it's a matter of individual preference.
If you are already known professionally by a maiden name, it wouldn't make sense to change it, because you'd have to remarket yourself. Or if both partners are artists, then sometimes people prefer to have different names to avoid comparison. Using a maiden name certainly solves any problem if a divorce later happens, but it's hard to explain to a new partner because it implies a lack of belief in a relationship—which it isn't the issue it's tied into at all.
Your personal identity as an artist may be strongly tied to the name you've had since birth: Only you know how you wish to be considered.
What About Limited Edition Prints?
When you create a limited edition print, always indicate how many prints were made and the number of that particular print, for example, 3/25 (the third print of a total of 25). Sign it as well.